Abstract
Although some algebraic theories such as partial order set, lattice and their properties on fuzzy set had been studied, these algebraic theories on fuzzy automata (FA) have not been discussed at present. For saving the energy of the battery so as to make it play the best performance, this paper proposes first an algebraic system on a finite-state deterministic fuzzy automaton (FDFA), including the partial order set, lattice and its properties. Second, this paper constructs a detection model system to monitor the consumption of battery power, and the detection model consists of four parts, as well as including supervision function network and decision-making process. Third, this paper gives the whole dynamic process of consumption and consumption rate of battery power, as well as discusses the comparison of the detection accuracy of between the detection model and other detection methods in the battery power consumption by simulation. Through the homomorphism and the isomorphic mapping of the lattice, the partial state of the FDFA is studied to realize the function of the whole state. These research results will provide a theoretical reference, system modeling and application background for many departments such as control, detection, tracking, identification and so on.
Highlights
Until now, we had studied the logicality, computational power, recognition language, state transition, robustness and composition of deterministic or fuzzy automata [1], [19], [21]
The decision-making is implemented by the energy saving detection model base on homomorphic mapping of finite-state deterministic fuzzy automaton (FDFA) lattice as follows: When e (k) > δ in the formula (6), that is, when the state of charge (SOC) of the battery is an interval value, such as the interval value in Example 2 above, the detection model starts to charge the battery or add electrolyte to the battery and keep the battery working, or stop the operation of battery and make an alarm reminder
APPLICATIONS OF DETECTION MODEL BY FDFA The consumption process of battery power is from one energy state to another energy state at all times, and the set that consists of any two energy states of the battery has the minimum upper bound and the maximum lower bound in any a time period
Summary
We had studied the logicality, computational power, recognition language, state transition, robustness and composition of deterministic or fuzzy automata [1], [19], [21]. B. LATTICE OF FUZZY AUTOMATA The subset (GT , T ) of element (G0, F) of partial order FDFA does not necessarily has the minimum upper bound or the maximum lower bound. If the subset that consists of any two elements in (G0, F) of M has the minimum upper bound and the maximum lower bound, M or (G0, F) regarding the partial order relation (⊆, ≤) is called a lattice, labeled as the lattice M , (⊆, ≤) or (G0, F) , (⊆, ≤). Definition 7: The final state fuzzy set (G0, F) of FDFA M has two binary operations ∨ |∪ and ∧ |∩ which satisfy (L1) ∼ (L4), (G0, F) , ∨ |∪ , ∧ |∩ or M , ∨ |∪ , ∧ |∩ is called a lattice. The converter system has achieved good stability under the FDFA homomorphic mapping detection, and the supervision function network improves the tracking performance of the system and reduces the steady-state error of the system by compensating for the nonlinear detected object
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
